The Brunn-Minkowski inequality

被引：581

作者：

Gardner, RJ ^{[1
]}

机构：

[1] Western Washington Univ, Dept Math, Bellingham, WA 98225 USA

来源：

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY | 2002年 / 39卷 / 03期

关键词：

Brunn-Minkowski inequality; Minkowski's first inequality; Prekopa-Leindler inequality; Young's inequality; Brascamp-Lieb inequality; Barthe's inequality; isoperimetric inequality; Sobolev inequality; entropy power inequality; covariogram; Anderson's theorem; concave function; concave measure; convex body; mixed volume;

D O I：

10.1090/S0273-0979-02-00941-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In 1978, Osserman [124] wrote an extensive survey on the isoperimetric inequality. The Brunn-Minkowski inequality can be proved in a page, yet quickly yields the classical isoperimetric inequality for important classes of subsets of R-n, and deserves to be better known. This guide explains the relationship between the Brunn-Minkowski inequality and other inequalities in geometry and analysis, and some applications.

引用

页码：355 / 405

页数：51

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